THE TYPE I HEAVY-TAILED ODD POWER GENERALIZED WEIBULL-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS

Abstract

In this study, we propose a new heavy-tailed distribution, namely, the type I heavy-tailed odd power generalized Weibull-G family of distributions. Several statistical properties including hazard rate function, quantile function, moments, distribution of the order statistics and Rényi entropy are presented. Actuarial measures such as value at risk, tail value at risk, tail variance and tail variance premium are also derived. To obtain the estimates of the parameters of the new family of distributions, we adopt the maximum likelihood estimation method and assess the consistency property via a Monte Carlo simulation. Finally, we illustrate the usefulness of the new family of distributions by analyzing four real life data sets from different fields such as insurance, engineering, bio-medical and environmental sciences.